A New Approach For Solving The Two Dimensional One Phase Stefan Problem With Boundary Temperature

This paper is devoted to a new approach for solving two dimensional one-phase Stefan problem with boundary temperature. We turn attention to the moving melt interface between the liquid and the solid for nanoscaled particles.We have presented the analytic method for the one-phase Stefan problem which expected to exist for all domain. This analytic method based on Green's function for the heat equation in the domain Dr 0, 0 0 , ( 0 0 ) and is required a good deal of the heat potential theory. For two independent unknown thermodynamical parameters (temperature and phase function) Green’s function has played a prominent role for the obtained integral representation of temperature field and description of behavior of the phase transition temperature motion. We consider a two-dimensional heat equation with the initial and fixed boundary conditions. Then, using this defined Green’s function and its properties, we define integral representatives of the temperature distributions and the law of motion of the diving boundary for the onephase Stefan problem. The existence, uuniqueness and regularity theorem of the constructed analytic solution with the diving boundary have been proved in the weighted Sobolev spaces. Keywords— Stefan problem, Free boundary, Heat equation, Green’s function, Irregular boundary, Analytical solution.